Question

The annual nominal interest rate on the unpaid portion of a contract is 17%. If the interest is compounded quarterly, the effective interest rate is most nearly:

A) 14%
B) 16%
C) 18%
D) 20%

Answer 1

The effective interest rate with a nominal annual interest rate of 17% compounded quarterly is approximately 18.09%. This is calculated using the formula for effective annual interest rate (EAR), resulting in Option C (18%) as the closest answer.

Step-by-step explanation:

The question asks for the calculation of the effective interest rate when the nominal interest rate is compounded quarterly. Given a nominal annual interest rate of 17%, compounded quarterly, the effective annual interest rate (EAR) can be calculated using the formula:

EAR = (1 + (i/n))^n - 1

Where i represents the nominal interest rate and n represents the number of compounding periods per year. In this case:

• i = 0.17 (or 17%)
• n = 4 (since interest is compounded quarterly)

Now we can substitute the values into the formula:

EAR = (1 + (0.17/4))^4 - 1

EAR = (1 + 0.0425)^4 - 1

EAR = (1.0425)^4 - 1

EAR = 1.180945 - 1

EAR = 0.180945

That means the effective annual interest rate is approximately 18.09%, which is most nearly 18% (Option C).